Finite Group Databasebeta

← Group #13024672

Character table — Group #13024672

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101016161616161616161616161616161620202020202020404040404040404040408080808080
order12222244510101010101010444444420202020202020202020202020202222444448888888844444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ411111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iii
χ5111111111111111111-1-111-1-1-1-1-1111111-1-1-1-11111111-1-111111111-1-1-1-1-1
χ6111111111111111111-1-111-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ9111111-1-1111111111-11111-1-1-1-1-111-1-1-1-1111111-1-11-1-111ii−i−iii−i−i-1i−ii−i
χ10111111-1-1111111111-11111-1-1-1-1-111-1-1-1-1111111-1-11-1-111−i−iii−i−iii-1−ii−ii
χ11111111-1-1111111111-111-1-1-1-1-1-1-111-1-1-1-11111-1-111-111-1-111-1-1-1-11111-1-11
χ12111111-1-1111111111-111-1-1-1-1-1-1-111-1-1-1-11111-1-111-111-1-1-1-11111-1-11-111-1
χ13111111-1-1111111111-1-1-1111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1ii−i−iii−i−i1−ii−ii
χ14111111-1-1111111111-1-1-1111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1−i−iii−i−iii1i−ii−i
χ15111111-1-1111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1
χ16111111-1-1111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-11-1-11
χ172222222222222222-2-2002200000-2-2-2-2220000-2-2-2-2222000000000000000
χ182222222222222222-2-200-2-200000-2-2-2-22200002222-2-2-2000000000000000
χ19222222-2-222222222-22002200000-2-222-2-20000-2-2222-2-2000000000000000
χ20222222-2-222222222-2200-2-200000-2-222-2-2000022-2-2-222000000000000000
χ212-2-22-222-22-2-2-222-220000000000000002-200002-22-200000i2−i2i2−i2i2−i2i2−i200000
χ222-2-22-222-22-2-2-222-220000000000000002-200002-22-200000−i2i2−i2i2−i2i2−i2i200000
χ232-2-22-222-22-2-2-222-220000000000000002-20000-22-22000002−22−2−22−2200000
χ242-2-22-222-22-2-2-222-220000000000000002-20000-22-2200000−22−222−22−200000
χ252-2-22-22-222-2-2-222-22000000000000000-2200002-2-22000002−2−222−2−2200000
χ262-2-22-22-222-2-2-222-22000000000000000-2200002-2-2200000−222−2−222−200000
χ272-2-22-22-222-2-2-222-22000000000000000-220000-222-200000i2−i2−i2i2−i2i2i2−i200000
χ282-2-22-22-222-2-2-222-22000000000000000-220000-222-200000−i2i2i2−i2i2−i2−i2i200000
χ2944444444-1-1-1-1-1-1-1-14444004-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-400-41111-1-1-1-1-1-111110000000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-40000055−5−51111-1-155−5−50000000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-400000−5−5551111-1-1−5−5550000000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-44400-41111-1-11111-1-1-1-10000000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-4-4-4004-1-1-1-1-1-1111111110000000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-440000055−5−511-1-111−5−5550000000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-4400000−5−55511-1-11155−5−50000000000000000000000
χ374444-4-40044-4-4-4-4440000440000000000000000000-400000000000000000
χ384444-4-40044-4-4-4-4440000-4-40000000000000000000400000000000000000
χ394-44-400004-400004-4002i−2i4-4000000000002i−2i2i−2i00000002i−2i0000000000000
χ404-44-400004-400004-4002i−2i-44000000000002i−2i2i−2i0000000−2i2i0000000000000
χ414-44-400004-400004-400−2i2i4-400000000000−2i2i−2i2i0000000−2i2i0000000000000
χ424-44-400004-400004-400−2i2i-4400000000000−2i2i−2i2i00000002i−2i0000000000000
χ434-4-444-4004-444-4-4-44000000000000000000000000004i−4i000000000000000
χ444-4-444-4004-444-4-4-4400000000000000000000000000−4i4i000000000000000
χ458888-8-800-2-22222-2-20000000000025−25000000000000000000000000000000
χ468888-8-800-2-22222-2-200000000000−2525000000000000000000000000000000
χ4788-8-80000880000-8-80000000000000000000000000000000000000000000
χ4888-8-80000-2-225−2525−252200000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000
χ4988-8-80000-2-225−2525−25220000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000
χ5088-8-80000-2-2−2525−2525220000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000
χ5188-8-80000-2-2−2525−25252200000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000
χ528-88-80000-2225−25−2525-22004i−4i0000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000
χ538-88-80000-2225−25−2525-2200−4i4i00000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000
χ548-88-80000-22−252525−25-22004i−4i0000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000
χ558-88-80000-22−252525−25-2200−4i4i00000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000
χ568-8-888-800-22-2-2222-200000000000002i5−2i50000000000000000000000000000
χ578-8-888-800-22-2-2222-20000000000000−2i52i50000000000000000000000000000
χ588-8-88-888-8-2222-2-22-2000000000000000-2200000000000000000000000000
χ598-8-88-88-88-2222-2-22-20000000000000002-200000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.